Does Earth's Gravity Do Work on Satellites?

[putongren]

Does the gravity of Earth do any work on satellites orbiting the planet, assuming perfect circular orbit?

General Definition of work: W=(line integral) F * ds , F=force vector, ds=infinitesimal displacement vector, *=dot product.

We know that in circular motion, the velocity vector is always perpendicular to the centripetal acceleration (I think we assume that centripetal acceleration is equated to gravitational acceleration), so 0 = F * v for all positions. so that means that 0 = F * ds/dt. If F * ds =0 for all positions, then W = 0. Does 0 = F * ds/dt imply F * ds = 0?

Thank you.

 

[D H]

Correct.

 

[A.T.]

Does the gravity of Earth do any work on satellites orbiting the planet, assuming perfect circular orbit?

Perfect circular orbit means: potential energy doesn't change and kinetic energy doesn't change so there is no work to do.